Central Limit Theorem for a conditionally centred functional of a Markov random field

Carlo Gaetan , Xavier Guyon (1, 2)

1 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique

We prove a CLT for empirical sums of a conditionally centred functional of a MRF on a non necessarly regular set of site. Since positive definiteness of the variance of the sums is crucial, we introduce the notion of conditionally separating partition and we give tools to verify such a positive definiteness. Exemples of Ising and gaussian MRF are studied.

Mots clés: Central Limit Theorem; Markov random field; Ising model; Gaussian field; conditionally centred functional; irregular lattice

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Carlo Gaetan, Xavier Guyon. Central Limit Theorem for a conditionally centred functional of a Markov random field. 2004. ⟨hal-00272423⟩